timeintegrated

Timeintegrated refers to a quantity that has been obtained by integrating a signal or rate over a period of time. In mathematical terms, if f(t) represents a time-dependent signal, the timeintegrated value over an interval [t0, t1] is TI = ∫_{t0}^{t1} f(t) dt. The concept is used across science to summarize temporal behavior in a single scalar.

Time integration contrasts with time-resolved measurements, which preserve temporal structure such as decay curves, arrival times, or oscillations. Time-integrated data trades temporal detail for higher signal-to-noise or simpler interpretation, and is often sufficient when lifetime information is not needed or when the instrument cannot resolve fast dynamics.

In spectroscopy and fluorescence, time-integrated intensity is the total emitted light collected during a detection window, and can be proportional to concentration times quantum yield, assuming stable dynamics and known detection efficiency. In high-energy physics, integrated luminosity (often written as Lint) represents the total collision flux over a data-taking period; the expected number of events is N = σ Lint, with σ the process cross section.

In practice, the limits of integration may be chosen to match the experimental gate or observation window, and for discrete data TI ≈ ∑ f(ti) Δt. The term also appears in contexts such as time-integrated spectra, time-integrated response, and time-integrated cross sections, where the goal is to summarize a time-dependent phenomenon with a single measure.

See also: time-resolved, luminescence, fluorescence, cross section, luminosity.